The following is true:

• Necessary and sufficient for chirality is the absence of an axis of rotoreflection.
  Or conversely:
• Necessary and sufficient for achirality is the presence of an axis of rotoreflection.
  Or:

• An object is chiral if and only if it does not contain an axis of rotoreflection.

Since = S₁ and i = S₂, the above mentioned observations on mirror plane and center of inversion are implied in this theorem as special cases.

There is only one disadvantage of this criterion, the fact that most of us are not familiar with axes of rotoreflection.